Interestingly, the variational lower bound derived using the conjugate function approach corresponds to the scalar case of \(I_{TUBA}\)  in [1]}, obtained from the inequality \(\log (x)\le \frac{x}{a}+\log (a)-1\)  and with the substitution \(f(\mathbf {x},\mathbf {y}) = \log (D(\mathbf {x},\mathbf {y}))\) . Moreover, the maximization of the special case \(\mathcal {J}_{1}\)  leads to \(I_{NWJ}\)  [2]}.
